Cellular Automata

Testing is a key issue in the design and production of digital circuits and the adoption of Built-In Self Test techniques is increasingly popular. This paper shows an application in the field of Electronic CAD of the Selfish Gene algorithm, an evolutionary algorithm based on a recent interpretation of the Darwinian theory. A three-phase optimization algorithm is exploited for determining the structure of a Built-In Self Test architecture that is able to achieve good fault coverage results with a reduced area overhead.

Models of multi-agent systems usually update the states of all agents synchronously, but in many real life systems, agents behave asynchronously. Relatively little is yet known about the dynamic characteristics of asynchronous systems. Here we compare synchronous, random asynchronous, and ordered asynchronous updating schemes. Using one-dimensional (1D) cellular automata as a case study, we show that the type of update scheme strongly affects the dynamic characteristics of the system. We also show that global synchronisation can arise from local temporal coupling. Furthermore, it is possible to switch between chaotic, cyclic and modular behaviour by varying a single parameter, which suggests a possible mechanism by which environmental parameters influence emergent structure. We conclude that ordered asynchronous processes with local temporal coupling play a role in self-organisation within many multi-agent systems.

In this paper we will attempt to classify Lindenmayer systems based on properties of sets of rules and the kind of strings those rules generate. This classification will be referred to as a ‘parametrization’ of the L-space: the L-space is the phase space in which all possible L-developments are represented.

This paper is an attempt to explore and to propose a model of interactions between social, environmental and economic variables in land-use and urban development dynamics, using cellular automata. Such models can simulate spatial evolutions with different development perspectives and can produce future development scenarios useful for decision-making processes. For the purposes of this study, a cellular automaton applied in the City of Heraklion (Crete) has been developed. The implementation of the model hereby illustrated is a pilot experience and still in a groundwork phase. However, we believe that this paper, addressing few methodological, theoretical and practical issues, offers an unpretentious, but useful contribution for cellular automata based modelling, and more importantly, suggests why such models are particularly useful for urban simulations.

We propose a theory of deterministic chaos for discrete systems, based on their representations in binary state spaces $ \Omega $, homeomorphic to the space of symbolic dynamics. This formalism is applied to neural networks and cellular automata; it is found that such systems cannot be viewed as chaotic when one uses the Hamming distance as the metric for the

In this paper we use the Cellular Automata integrated with Finite Element method (CAFE) to account for the effect of microstructure on quasi-brittle properties within a finite element simulation.  Here the microstructure is modeled explicitly by subdividing a finite element into small elements called cells.  The heterogeneous microstructure is created from key cells, called seeds, from which particle-like regions may be grown with defined characteristics.  By this topological approach we obtain sets of cells with variable properties to model the microstructure (rules are enforced during the selection of the seeds to avoid overlap between particles).  Graded microstructures, textures and particle anisotropy can be readily simulated in microstructures with multiple phases.  The influence of the initial finite element mesh is erased during the development of the microstructure. A mesh-free framework has been developed to compute the fracture development through the microstructure, using cellular automata to calculate the damage to the microstructure. With this method, we can study the development of discontinuous cracking and fracture, and its sensitivity to microstructure.

Watershed management and early warning flood forecasting system is becoming more and more important especially in relation to anticipated climate change. The characteristics and the validation of the Cetemps HYdrological Model (CHYM) developed by the hydrological group of the Cetemps Center of Excellence are described. CHYM is a grid based model and the main physical processes concerning the hydrological cycle are implemented in the model (Todini and Ciarrapica, 2002; Sorooshian et al., 1995). In the preprocessing phase different data sources are assimilated by the model in order to reconstruct precipitation field on the area of interest. At the moment the available data are the observed rain gauge values, the forecasted MM5 precipitation fields and the satellite rainfall estimation (Grimes et al., 2003). This multisources data acquisition system using observed and forecasted data makes it possible to simulate a time window that span from few days before the event to few days after....

This paper presents applications in which Electron Beam Induced Deposition (EBID) is used to characterize, analyze, and fabricate, nanostructures and devices. High aspect ratio Cylindrical Ultra Sharp (CUS) Atomic Force Microscope (AFM) probe tips are grown on discarded AFM tips using EBID. AFM is done using these CUS probe tips and compared to standard commercially available AFM probes as a baseline. The use of EBID to deposit platinum nanodots on thin foils for use as a hard mask in the fabrication of Quantum Cellular Automata cell structures is also reported. Successful EDS analysis was performed on these nanodots in a conventional Scanning Electron Microscope (SEM) with a high spatial resolution normally found only in the Scanning Transmission Electron Microscope (STEM). These EDS results demonstrate the ability to capture pertinent material properties of nanostructures in a more manageable SEM, and therefore, forgo the necessary complexities associated with a standard STEM.

This paper investigates preimages (ancestors or past configurations) of specified configurations of one-dimensional cellular automata. Both counting and listing of preimages are discussed. The main graphical tools used are the de Bruijn diagram, and its extension the preimage network, which is created by concatenating de Bruijn diagrams. The counting of preimages is performed as multiplication of topological matrices of de Bruijn diagrams. Listing of preimages is described using two algorithms. The first algorithm traces paths in the preimage network and focuses on local knowledge of the network. The second performs a complete analysis of the network before proceeding with listing.

Mathematical models have a long history of use for understanding ecological systems. In a recent book, A New Kind of Science, Steve Wolfram calls into question traditional modeling approaches and calls for the increased application of cellular automata (CA) models in all areas of scientific inquiry. With reference to Wolfram's book, we review the past uses of CA models in ecology and discuss the relative utility of using traditional models versus CA models to understand ecological communities.

In urban systems modeling, there are many elaborate dynamic models based on intricate decision processes whose simulation must be based on customized software if their space±time properties are to be explored eectively. In this paper we present a class of urban models whose dynamics are based on theories of development associated with cellular automata (CA), whose data is ®ne-grained, and whose simulation requires software which can handle an enormous array of spatial and temporal model outputs. We ®rst introduce the generic problem of modeling within GIS, noting relevant CA models before outlining a generalized model based on Xie's (1996, A general model for cellular urban dynamics. Geographical Analysis, 28, 350±373)``dynamic urban evolutionary modeling'' (DUEM) approach. We present ways in which land uses are structured through their life cycles, and ways in which existing urban activities spawn locations for new activities. We de®ne various decision rules that embed distance and direction, density thresholds, and transition or mutation probabilities into the model's dynamics, and we then outline the software designed to generate eective urban simulations consistent with GIS data inputs, outputs and related functionality. Finally, we present a range of hypothetical urban simulations that illustrate the diversity of model types that can be handled within the framework as a prelude to more realistic applications which will be reported in later papers. # Computers, Environment and Urban Systems 23 (1999) 205±233 www.elsevier.com/locate/compenvurbsys 0198-9715/99/$ -see front matter # 1999 Published by Elsevier Science Ltd. All rights reserved. P I I : S 0 1 9 8 -9 7 1 5 ( 9 9 ) 0 0 0 1 5 -0

In this paper we report on the synthesis of sounds using cellular
automata, specifically the multitype voter model. The mapping process adopted is based on digital signal processing analysis of automata evolutions and consists in mapping histograms onto spectrograms. The main problem of cellular automata is the difficulty of control and, consequently, sound synthesis
methods based on these computational models normally present a high factor of randomness in the output. We have achieved a significant degree of control as to predict the type of sounds that we can obtain. We are able to develop a flexible sound design process with emphasis on the possibility of controlling over time the spectrum complexity.

Digital Image Scrambling (DIS) means creating confusion in image elements to make the information look random by reordering and changing the position of image pixels. Cellular Automata (CA) appear as natural tools for image processing due to their spatial topology, local interaction of cells and simple parallel computational implementation. In recent years, many Cellular Automata-Based Image Scrambling algorithms have been proposed to protect digital images. The aim of this paper is to review several image scrambling algorithms based on elementary Cellular Automata (ECA) and Two-Dimensional Cellular Automata (2D-CA). Simulations of these DIS algorithms in Matlab software are used to obtain the scrambling degree. The effect of different boundary conditions and CA-generations on scrambling degree is also evaluated. We further analyze the computational effort required by these algorithms. Experimental results reveal ECA-Based DIS algorithm results in better scrambling degree compared to 2D-CA Based DIS algorithms under study.

The research project presented in this paper deals with the development of a creative evolutionary design methodology for layout problems in architecture and urban planning. To date many optimisation techniques for layout problems have already been developed. The first attempts to automate layout were undertaken back in the early 1960s. Since then, these ideas have been taken forward in various different manifestations, for example shape grammars, CBS, cellular automata and evolutionary approaches. These projects, however, are mostly restricted to very specific fields or neglect the creative, designerly component. Since pure optimisation methods are of little practical use for design purposes, there have been no useful attempts to derive a universally applicable method for computer aided layout design. For this we need to be aware that designing is a process that occurs at different levels and degrees of abstraction. The solution space is explored in the realm between intuition and rationality in a variety of ways. Good solutions can only arise through an intensive and fluid dialogue between the designer and the generating system. The goal of our project is to develop an adaptive design system for layout problems. To this end we examine different approaches to achieving the best possible general applicability of such a system and discuss criteria that are crucial for the development of such systems.

Quantum-dot Cellular Automata (QCA) has been widely advocated as a new device architecture for nanotechnology. QCA systems require extremely low power, together with the potential for high density and regularity. These features make QCA an attractive technology for manufacturing memories in which the paradigm of memory-in-motion can be fully exploited. This paper proposes a novel serial memory architecture for QCA implementation. This architecture is based on utilizing new building blocks (referred to as tiles) in the storage and input/output circuitry of the memory. The QCA paradigm of memory-in-motion is accomplished using a novel arrangement in the storage loop and timing/clocking; a three-zone memory tile is proposed by which information is moved across a concatenation of tiles by utilizing a two-level clocking mechanism. Clocking zones are shared between memory cells and the length of the QCA line of a clocking zone is independent of the word size. QCA circuits for address decoding and input/output for simplification of the Read/Write operations are discussed in detail. An extensive comparison of the proposed architecture and previous QCA serial memories is pursued in terms of latency, timing, clocking requirements, and hardware complexity.

A largely phenomenological study of two-dimensional cellular automata is reported. Qualitative classes of behavior similar to those in one-dimensional cellular automata are found. Growth from simple seeds in two-dimensional cellular automata can produce patterns with complicated boundaries, characterized by a variety of growth dimensions. Evolution from disordered states can give domains with boundaries that execute effectively continuous motions. Some global properties of cellular automata can be described by entropies and Lyapunov exponents. Others are undecidahle.

It is well-known that big cities suffer from traffic congestion and all consequences that come with it. This is an especial problem in cities in developing countries where the public transportation system is not reliable and where the fleet of vehicles tend to be old thus increasing air pollution. There is no turnkey solution for this problem, but several improvements have been suggested in the field of urban and traffic management, provided an information system is built which can provide information to both the traffic experts and the user of the system. Such an information system has to incorporate features of an ITS and an ATIS. An underline assumption is that there is a simulation model to provide certain kinds of information in forecast. This paper discusses the model and implementation of such an information system which is based on a microscopic model of simulation and on cellular automata and is implemented using agent technologies and with a bottom-up philosophy in mind. We give here an overview of the project, the details of the modules (data, simulation, driver and information/visualization), as well as discuss an application of the simulation tool.

This paper is an attempt to explore and to propose a model of interactions between social, environmental and economic variables in land-use and urban development dynamics, using cellular automata. Such models can simulate spatial evolutions with different development perspectives and can produce future development scenarios useful for decision-making processes. For the purposes of this study, a cellular automaton applied in the City of Heraklion (Crete) has been developed. The implementation of the model hereby illustrated is a pilot experience and still in a groundwork phase. However, we believe that this paper, addressing few methodological, theoretical and practical issues, offers an unpretentious, but useful contribution for cellular automata based modelling, and more importantly, suggests why such models are particularly useful for urban simulations.

This paper describes a method for modeling the natural peeling phenomenon over any 3D surface. Using crack input data-precomputed with a semi-physical solution-this method allows simulating peeling on any type of triangulated 3D object. Our model's main advantage is that it proposes an method that is intuitive enough to make it easy to understand and convenient to apply, user controllable, and easily extensible-especially to simultaneous natural phenomena. We first introduce the general development of peeling over various materials. Then, we present how to define groups of peeling, how to determine a realistic and natural peeling order, and how to simulate the rendering of two types of special peelings. Finally, a set of graphical results concludes the paper, presenting a series of direct peeling and curling patterns using classical paintings or plastic-paintings simulated materials.

This paper proposes a new way to study traffic flow at an urban unsignalised intersection, through detailed space considerations, using cellular automata (CA). Heterogeneity and inconsistency are simulated by incorporation of different categories of driver behaviour and reassignment of categories with given probabilities at each time step. The method is able to reproduce many features of urban traffic, for which gap-acceptance models are less appropriate. Capacities of the minor-stream in a TWSC intersection are found to depend on flow rates of major-streams, also changes with flow rate ratio (FRR= flow rate of near lane: flow rate of far lane). Hence flow rates corresponding to each stream must be distinguished. The relationship between the performance of intersections and other traffic flow parameters is also considered. Vehicle movements in this paper relate to left-side driving, such as found in UK/Ireland. However, rules are generally applicable.

Most of the conventional traffic Cellular Automaton (CA) models based on the Nagel-Schreckenberg model (NaSch model) have two problems: an unrealistic deceleration dynamics when a vehicle agent collides with a preceding vehicle in a stopping event, and the problem with reproducing the synchronized flow in Kerner's three-phase theory. In this paper, a revised stochastic Nishinari-Fukui-Schadschneider (S-NFS) model, belonging to the class of NaSch models, is presented. The proposed CA model, where a random braking effect is improved by considering the dependency on the velocity difference and heading distance with a preceding vehicle, is confirmed to overcome the two above-mentioned drawbacks.

Remotely-sensed images and Geographical Information Systems (GIS) data were integrated into the SLEUTH cellular automata (CA) model to analyze land –use/landcover dynamics in Chiang Mai city and its surrounds. The land-use and land-cover statistics, obtained from GIS data base and satellite images from 1952, 1977, 1989 and 2000 revealed rapid increased in urbanization during these periods. To understand the underlying causes of landuse and land-cover dynamics, remote sensing, GIS and modeling techniques were applied. The SLEUTH model contains a characteristic that offers advantages in integrating with raster-based remote sensing data and in increasing the capability of GIS in modeling the spatial dynamics. The objectives of this research are (1) to systematically analyze remotelysensed images of Chiang Mai area from available time series into major landuse-land -cover types and to identify the significant landuse/landcover changes; (2) to apply a GIS for capturing the information on...

In ourpaper we would like to present afuuijied cellular automata structure called fuzzy cellular automata. We begin ourpaper with afuuijied entity calledfuzzy automaton, then we present basics of cellular automata andjinally we define fuzzy cellular automata. At the end we present some simulation results from the field of$re spread in homogenuous nature environment.

Structural properties of two well-known families of keystream generators, Shrinking Generators and Cellular Automata, have been analyzed. Emphasis is on the equivalence of the binary sequences obtained from both kinds of generators. In fact, Shrinking Generators (SG) can be identified with a subset of linear Cellular Automata (mainly rule 90, rule 150 or a hybrid combination of both rules). The linearity of these cellular models can be advantageously used in the cryptanalysis of those keystream generators.

A more correct way to understand De Broglie in terms of equivalence instead of duality. We regard two things to be equivalent if they are quantitatively identical while being qualitatively different. This definition is not given in the actual paper. I'll give a more rigorous definition like this in subsequent works. Thanks.

Integrable cellular automata (CAs) are discrete dynamical systems that possess many attributes of integrability as for example conserved quantities, symmetries and localized solutions. They constitute an answer to the general problem: how to discretize a given integrable system of differential equations, maintaining the integrability property. This answer suggests that integrability of discrete systems and their coherent structures are inherently connected with the iterated string processing performed by automata. The propagating solutions (so-called coherent objects) on certain cellular automata have been found to exhibit nondestructive collisions similar to those observed for soliton systems like the Korteweg-de Vries Equation. In such cases, pulse-like disturbances propagating along a uniform nonlinear medium are represented by strings of symbols (e.g. zero-one patterns), passing through a one-way structure – the pipeline of identical automata M. The analysis of these moving objects reduces to investigating the repeated automaton action over strings, also called an iterated automaton map (IAM); M(a t) = a t+1 , t = 0, 1, …. All known models capable of supporting such discrete localized structures are described by automata (Siwak, 2001, 2002), and a method (called ultra-discretization) leads to discrete systems in which solutions of some familiar soliton equations are preserved as soliton-like patterns (Tokihiro & Nagai & Satsuma, 1999). This means that IAM is a fundamental discrete mechanism that supports localized soliton-like periodic structures. This is why a new term iterons (Siwak, 2001, 2002) has been proposed for these objects. Note, that also fractals owe their existence to the iterating process of some maps. There are two classes of iterons. The first one consists of particles well known in cellular automata models (Delorme & Mazoyer, 1999) where the parallel processing of strings occurs. The second class is not widely known and consists of so-called filtrons. The filtrons are emergent coherent objects occurring in serial processing of strings (Siwak, 2001). In parallel processing of a string a t given at time t all symbols 1 + t i a of the next string a t+1 are updated simultaneously e.g. by the function 1 + t i a = f(t r i a − , …, t i a , ..., t r i a +). When the same function f is used for all positions i, one has just 1-dimensional CA; with f being called its local function or rule. The arguments of f are determined by so-called neighborhood window N i = (-r, …, +r); here N i designates at r neighbors at the both sides of position i. The listing of consecutive strings a t for t = 0, 1, … one under another forms what is called space-time (ST) diagram. This diagram visualizes the evolution of given string a 0 – the dynamics of CA system in phase space for initial global state a 0. Occasionally, some moving and periodic patterns of symbols or segments of a string are seen on ST diagrams of CA processing. These are just particles or signals of CAs (Delorme & Mazoyer, 1999). The serial processing of strings is performed by the computational model called finite (state) automaton. Let us recall that Mealy type automaton is described by M = (S, Σ, Ω, δ, β, s 0) where S, Σ and Ω are nonempty finite sets of respectively states, inputs and outputs, δ : S × Σ → S is called the next state function of M, β : S × Σ → Ω is called the output function of M, and s 0 is the initial (extinction) state of automaton. The automaton converts sequences of symbols, preserving their length. Any input string is read sequentially from left to right, one symbol at each instant τ of time (pulse of clock). For all τ = 1, 2, … the automaton:-reads input symbol σ(τ),-changes its current state s(τ) onto the next one according to δ (s(τ), σ(τ)) = s(τ+1), and-generates the symbol β (s(τ), σ(τ)) = ω(τ) of resulting string. Thus the complete one step conversion a t → a t+1 requires a series of clock pulses τ. To consider IAMs one has to assume the unified input-output alphabet A = Σ = Ω = {0, 1, …, m}.

We present a solution to the Firing Squad Synchronization Problem that works both in Von Neumann and Moore neighborhood and whatever is the dimension of the space. That solution is based on fields that provide a clean modular decomposition of such cellular automata problem.

Using cellular automata (CA) Nagel-Schreckenberg (NaSch) model, we numerically study the probability P ac of the occurrence of car accidents at nonsignalized intersection when drivers do not respect the priority rules. We also investigated the impact of mixture lengths and velocities of vehicles on this probability. It is found that in the¯rst case, where vehicles distinguished only by their lengths, the car accidents start to occur above a critical density c . Furthermore, the increase of the fraction of long vehicles (F L ) delays the occurrence of car accidents (increasing c ) and increases the risk of collisions when > c . In other side, the mixture of maximum velocities (with same length for all vehicles) leads to the appearance of accidents at the intersection even in the free°ow regime. Moreover, the increase of the fraction of fast vehicles (F f ) reduces the accident probability (P ac ). The in°uence of roads length is also studied. We found that the decrease of the roads length enhance the risk of collision.

We study the dynamical behavior of D-dimensional linear cellular automata over Zm. We provide an easy-to-check necessary and sufficient condition for a D-dimensional linear cellular automata over Zm to be ergodic and topologically transitive. As a byproduct, we get that for linear cellular automata ergodicity is equivalent to topological transitivity. Finally, we prove that for 1-dimensional linear cellular automata over

Church’s and Turing’s theses assert dogmatically that an informal notion of effective calculability is captured adequately by a particular mathematical concept of computabilty. I present analyses of calculability that are embedded in a rich historical and philosophical context, lead to precise concepts, and dispense with theses. To investigate effective calculability is to analyze processes that can in principle be carried out by calculators. This is a philosophical lesson we owe to Turing. Drawing on that lesson and recasting work of Gandy, I formulate boundedness and locality conditions for two types of calculators, namely, human computing agents and mechanical computing devices (or discrete machines). The distinctive feature of the latter is that they can carry out parallel computations. Representing human and machine computations by discrete dynamical systems, the boundedness and locality conditions can be captured through axioms for Turing computors and Gandy machines; models o...

We live in the era of information explosion and have witnessed the trend of leveraging cloud-based services for large scale content storage, processing, and distribution. Data security and privacy are among top concerns for any business environments. As more and more security breaches happening all over the world in different forms as a threat to the information industry, the end user should have the protection and privilege of secured access. Chaos possesses many interesting properties, such as deterministic but random like complex behavior, high sensitivity to initial conditions and system parameters and long term unpredictability. This paper introduces a cellular automata based chaotic encryption scheme and the results are comparable with well-known AES block cipher algorithm.

Pedestrian flow is inherently complex, more so than vehicular flow, and development of microscopic models of pedestrian flow has been a daunting task for researchers. This paper presents the use of Cellular automata (CA) microsimulation for modeling bi-directional pedestrian ...

Neural network" models of brain function assume neurons and their synaptic connections to be the fundamental units of information processing, somewhat like switches within computers. However, neurons and synapses are extremely complex and resemble entire computers rather than switches. The interiors of the neurons (and other eucaryotic cells) are now known to contain highly ordered parallel networks of filamentous protein polymers collectively termed the cytoskeleton. Originally assumed to provide merely structural "bone-like" support, cytoskeletal structures such as microtubules are now recognized to organize cell interiors dynamically. The cytoskeleton is the internal communication network for the eucaryotic cell, both by means of simple transport and by means of coordinating extremely complicated events like cell division, growth and differentiation. The cytoskeleton may therefore be viewed as the cell's "nervous system". Consequently the neuronal cytoskeleton may be involved in molecular level information processing which subserves higher, collective neuronal functions ultimately relating to cognition. Numerous models of information processing within the cytoskeleton (in particular, microtubules) have been proposed. We have utilized cellular automata as a means to model and demonstrate the potential for information processing in cytoskeletal microtubules. In this paper, we extend previous work and simulate associative learning in a cytoskeletal network as well as assembly and disassembly of microtubules. We also discuss possible relevance and implications of cytoskeletal information processing to cognition.

Cellular automata are models that deal with both nature and artefacts: they can indeed simulate living beings as well as be employed in the creation of objects. After the introduction of this concept by Stanislaw Ulam and John Von Neumann in the late 1940s, many different kinds of cellular automata have been created and have become part of what Christopher Langton called " artificial life " in 1986. The most complex examples among them are based on stochastic development, thus they share their structural properties with morphogenetic models like the one suggested by Alan Turing (1952). This is the reason why some cellular automata are capable of simulating the development of living beings , but also of cities and artefacts. They are indeed widely used in computer graphics related to parametric design, in order to create performative objects at various scales that can be produced according to the principle of mass customisation. The purpose of this study is to analyse the properties of these models with the help of computer simulations and, as a consequence, to explore some of their different fields of application. As a result, it can be observed that these processes , based on a stochastic geometry, can lead not only to simple biomimicry (regarded as the artificial replication of biological features) but also, in a wider sense, to bioinspiration (a more general relation between nature and artefacts based on shared structural properties).